Frequencies of Continuous Plates by Moment‐Ratio Method

Abstract

The moment‐ratio method developed is a numerical procedure to determine the natural frequencies of continuous orthotropic and isotropic plates. The basic concept employs dynamic flexibility functions at the panel joints. The moment‐ratio function of a panel may be obtained from the transfer of the preceding one. A fixed number of computational steps equal to the number of panels is required for each cycle. One of the natural frequencies will be obtained when the terminal moment‐ratio vanishes. A sufficient number of times with assumed varying frequencies will determine one of the natural frequencies to a degree of desired accuracy. Three numerical examples are included. Some of the numerical solutions are compared with existing data. Four types of boundary conditions of continuous plates—partial constraint, simple‐simple, simple‐clamp, and clamp‐clamp—are developed. An equivalent analysis of continuous orthotropic and isotropic plate systems is presented and their numerical frequencies are compared. Frequency clusters formed in uniform systems are introduced in the moment‐ratio method.